Z7WYr
The United States Bridge Formula
z:z;::
m'l!!lIlII!'l!lR
Claude
s. Napier~ Jr.:!
Dr. J aIm. P. Eicher2
Major importance is placed on truck size and
weight issues by highway engh"1eers and officials,
legislative bodies, commercial truckers. the
manufacturers of heavy motor vehicles and
others. The issue of truck size and weight
regulation has and sti111s a very controversial one.
For the past 30 years, since the passage of the
Federal-aid Highway Act of 1956. the Federal
government has regulated truck size and weight
on the Interstate System. Our present Bridge
Formula was adopted for the Interstate System by
the Federal-aid Highway Amendments of 1974.
w == 500 (LN + 12N + 36)
N-l
W == overall gross weight on any group of two or
more consecutive axles to nearest 500
pounds.
L == distance in feet between the extreme of any
group of two or more consecutive axles.
N = number
of axles
consideration.
in
group
under
Before addressing the specifiCS of the Bridge
Formula. a little background on some of the
history of size and weight policy and legislation in
the United States may be helpful.
The problem now and always has been is how to
rationalize design load with safe load carrying
capacity or regulatory loading. Engineers in our
country have worked since before the turn of the
century to agree on an appropriate design vehicle.
or umbrella loading for bridge design. One of the
first issues faced by the members of the AASHO
Committee on Bridges and Structures after its
formation in 1921 was determination of design
vehicles for bridges. In the 1920's many bridge
engineers conSidered that a t..-uck With a total
weight of 10 tons (deSignated HIO) was adequate.
Later in the 1930's AASHO's bridge engineers
agreed that a total load of 15 tons (designated H 15)
was adequate. However, the Second World War,
with its great need for mobilization of the c.-ountry's
industrial and military might and consequent
increase in truck size, influenced AASHO's
decisionmakers to agree on an HS20-44 (H20-S16
original designation) truck in 1944. The "HS"
stands for "heavy semi" or "highway semi." The
"20" means that the tractor weighs 20 tons and
the "44" is the year the umbrella vehicle was
adopted. This loading was used for bridges that
would be included in the Interstate System. After
the war. there was a trend toward the use of
heavier loadings to design bridges on all highway
systems.
Today. most bridges on the highway systems are
designed for the HS20-44 truck and there is
discussion about a higher design load. like the
HS25 which some States are already us:lng.
The standard deSign 10ad:lng in the AASHO
(AASHTO) design specifications has been
increased in the past to accommodate the
evolution of heavier trucks and still protect our
existing highway system. The changes in design
loadmgs have required corresponding changes in
State poliCies and regulations. as wen as Federal
regulation. In 1932, AASHO issued its first policy
statement recommending the following weight
limitations:
Single axle - 16,000 lbs
Tandem axle (under 8' spacing) - Formula
Axle group - Formula
w=
C(L+ 4O}
(also known as the Gemeny formula)
w = total gross weight in pounds on any two or
more consecutive axles
1
Structural Engineer, Bridge Division, Office of Engineering. Federal Highway Administration.Washington, D.e.
2
Director. Office of Motor Carrier Transportation, Federal Highway Administration. Washington, D.C.
225
C:: a coefficIent to be determined by the
mdMdual States
L = the distance between the first and last axles
of the group of axles under consideration
A value of 700 was recommended for C, as the
lowest which should be imposed. Mr. Albin
Gemeny, Senior Stnlctural Engineer. U.S. Bureau
of Public Roads, had recommended the followl..ng
equations for W;
=
W 670 (1.+40) for HI 0 bridges
W = 1000 (L+40) for H15 bridges
W;;;:: 1300 (L+40) for H20 bridges
Since 1932, AASHO has subsequently issued
several other poliCies as follows:
1.
1942 Emergency Regulation
2.
1946
3.
few tests were made of bridges as part of t.'I1e
AASHO tests at Ottawa. illinois, using heavy
trucks exceeding the design loading to mduce
gradual failure. In October 1952, the Texas
Engineering Experiment Station of Texas MM
completed a research proJ ect on the "Method of
Converting Hea,,'Y Motor Vehicle Loads into
Equivalent Design Loads on the Basis ofMrudmum
Bending Moments" for the Bureau ofPubHc Roads.
The report presented the results obtained from a
rather extensive investigation of highway loads
and their stress producing effects on simple span
bridges of various lengths.
In July 1962. the Texas Transportation Institute
of Texas .MM completed a research project on the
"Truck Weight Trends Related to Highway
Structures." The objective of the research was to
develop a general formula that met the folloVili.ng
requirements:
1.
Can be adjusted to fit any deSired level of
heavy vehicle operation,
1963
2.
Will permit relatively heavy rude group loads.
4.
1964 Policy and Revision in 1968
3.
Will encourage the use of multiaxle vehicles.
5.
1973 - Truck limits same as 1963 Limits
4.
Will not only be in harmony wIth the
6.
1974
7.
New policy is currently being prepared.
A brief review of each policy may be of interest. On
May 17, 1942, AASHO recommended an interim
substitute policy that was applicable for the
duration ofthe war emergency. Then in August 1,
1946. the 1932 policy. the 1942 emergency
regulations. and results of extensive studies by
AASHO and others were formulated into a new
policy. The single axle load was increased to
18,000 Ibs .. the tandem axle retained at 32,000
Ibs .. and the gross weight of axle groups was based
on a table which was based on the formula
W:: 1025 (L + 24) - 3L2
economic principles of highway and bridge
provision, but will also improve the payload
opportunities for truckers through a freer
chOice of vehicle types.
The following general formula was developed:
W = A [f (NL) + BN + Cl
W = maximum load in pounds carried on any
group of two or more consecutive axles.
L == distance in feet between the extremes of any
group of two or more consecutive axles
N == number of axles
consideration.
226
in
group
under
A. B & C are constants which depend upon
quality of highway and bridge provision and
deSired level of heavy vehicle operation.
The rnaxL.-num gross weight was 73,280 Ibs. for
L = 57 feet.
Several :Important research proJects were initiated
in the 1950·s. The WASHO and AASHO road tests
were sta.rted in 1950. These were extensive tests
of pavement using test vehicles loaded with single
axles from 2.000 to 30,000 pounds and tandem
axles of 24,000 to 48,000 pounds. In addition. a
in which
f ==
some function involVing "N' and "L"
The formula could be readily adjusted to any level
of heavy motor vehicle operation as desired simply
by adjustL.,g the constants included in it. A
number of variations of the general formula were
investigated, but the following one was
recommended as the fonnula that appeared to be
best suited for determining and regulating
permissible vehicle weights. consistent with both
heavy vehicle operation and the then present day
highway provision.
W :: 500 (NL + 12N + 32)
N~l
The 1963 policy of AASHO recommended
permissible single axle loads of 20,000 pounds
and still lirr..ited tandem axle loads to 32,000
pounds. The gross weight on a group of axles was
based on this formula.
The axle group loading for N from 2 to 6 allowed a
considerable increase over that permissible by Llle
1946 AASHO policy. There were limitations to the
use of the formula based on H 15-44 design
bridges.
The AASHO policy of 1964 and revision in 1968
for axle loads and gross weight were the same as
stated in the 1963 policy recommendation. The
1974 policy recommended permissible single axle
loads of 20,000 pounds and tandem axle loads of
34,000 pounds. The maximum permissible axle
group weights were based on our current formula.
However, the maxL.'TIum permissible gross weight
was limited by allowable length and axle weight
controls for certain typical vehicle types.
MSHTO's new proposed policy adopts the Federal
weight limits for the Interstate System as its new
guidelines.
So far only the State highway departments
involvement in developing recommendations
regarding weight and size limitations have been
discussed. It should be noted that until 1956 there
were no Federal weight limits. However, the
Bureau of Public Roads was active in working with
the States and AASHO on t..ruck Size and weight
issues.
The first Federal size and weight laws were enacted
in 1956 when the Interstate System program was
first financed at significant levels. (The Federal-aid
Highway Act of 1956, Pub.L. 84-627, 70 Stat. 374).
The large finanCial interest in the Interstate
System was the expressed reason for Federal
involvement in vehicle size and weight regulation.
It was felt that if the Federal goveIT'.ment was to
pay 90 percent of the cost of the Interstate System,
then it was entitled to protection of its investment
against damage caused by heavy loads on the
highways.
The Federal sizes and weight provisions ill the
1956 Federal-aid Highway Act were limited to
weight and width restrictions on the Interstate
System. The weight limits (18,000 pounds on a
single axle, 32,000 pounds on a tandem axle and
73.280 pounds gross vehicle weight) were those
recommended in the 1946 AASHO policy.
Provision was made in a "grandfather clause"
permitting higher load values which were
authorized under State laws in effect on July 1.
1956. Section 108(k) of the same act directed that
road tests then undeIWay be expedited and the
Secretary of Commerce report to the Congress
making recommendations on maximum desirable
dimensions and weights.
In 1964 the Secretary of Commerce presented a
report on "Maximum Desirable Dimensions and
Weights of Vehicles Operated on the Federal-aid
System." The report was published as House
Document 354, 88th Congress, 2nd Session and
was based on studies conducted by the FHVilA's
predecessor. The Bureau of Public Roads in the
Department of Commerce. The report
recommended that larger vehicles be permitted on
Federal-aid highways over a period of years.
Specifically. it was recommended that the vehicle
width limit be increased to 102 inches and that
weight limits be raised to 20,000 pounds for single
axles, 34,000 pounds for tandem axles, with gross
vehicle weights to be determined by the formula
(Bridge Formula B)
W", 500 (NL + 12N + 36)
N-I
which is our current bridge formula. The
relationship between vehicle dimensions and
highway damage, highway improvement needs,
and highway cost allocation were explicitly noted
and Size and weight increases were to be
predicated on States instituting adequate
construction. reconstruction, and maintenance
programs.
Congress did not implement any recom mendations from the 1964 report untll1974 when
the trucking industry was hurt by fuel shortage
and programs to reduce fuel consumption, such
as the 55 m.p.h. speed limit. Effective January 4,
1975, the Federal-aid Highway Amendments of
1974 increased the maxrrnum permissible weight
limits for the Interstate System and adopted the
227
use of our present brtdge formula. The maximum
allowable single and ta.."1dem weights were raised
to 20,000 and 34,000 pounds respectively. and
gross vehicle weights were controlled by Bridge
Formula B to a maximum of 80,000 pounds. The
new limits were permissive and the states could
retain lower weIghts for the Interstate System
because of a second grandfather clause included
in the law which allowed the States to continue to
use bridge formulas different from Blidge Fonnula
B for determining the maximum gross vehicle
weights.
The Surface Transportation Assistance Act of
1982 significantly increased the Federal role in
regulating vehicle sizes and weights. It. eliminated
the barrier States and provided for a national
uniform vehicle axle and gross weight limits for the
Interstate System by requiring all States to adopt
the Brtdge Formula and axle and gross weight
limits.
So much for the background and "legislative
history" of vehicle size and weight. Consideration
will now be devoted to the purpose and particulars
of the current blidge formula. Enforcement of the
Federal weight BmUs and the Brtdge Formula
protect our Nation's interstate bridges by
controlling the vehicle loads. An important feature
of the bridge formula was supposed to be the
incentive to use longer vehicles with a greater
number of axles.
During the period 1974 to 1982, there has been
increasing emphasis on enforcement of the bridge
formula by the States which has revealed a
difficulty some vehicles have in complying with the
bridge formula . Entire segments of certain
industries like the construction industry and
short wheel base container and ta.T1ker haulers
cannot utilize full capacity effiCiency within the
requirements of the bridge formula. Also, fOTvery
long, many axle vehicles which are being studied
under the provisions of the STAA of 1982, the
formula would allow unreasonably high loads
should the current 80,000 lb. maximum gross
weight limit be increased or lifted. The expressed
concerns have generated strong congressional and
public interest which has stimulated the FHWA to
re-examine the premise of the bridge formula.
In May 1984, the FHWA awarded a research
contract entitled "Bridge Formula Development" to
Texas Transportation Institute (TTI) ofTexas A&M.
The objective of the research was to evaluate the
need and adequacy of the present blidge gross
weight formula and develop a bridge formula for
228
application to bridges designed for H 15 and 1-1S20
loadings. The intent was to more fully utilize the
capacity of existing bridges without Significantly
shortening the service life of any.
The study has resulted in the recommendation
that a new formula, independent of the number of
included axles on the vehjcle, replace the current
formula as follows:
W = (34 -I- L) 1000 lb.
W = (62 + L/2) 1000 lb.
8 ft. :f L:f 56 ft.
L~ 56 ft.
Figure 1 shows a comparison of the proposed
bridge formula to the existing bridge formula. In
comparing the proposed formula vnth the current
formula. 3, 4 and 5 axle vehicle load limits are
generally increased by the proposed formula.
except for the shorter axle groupings, whereas 6,
7, 8 and 9 axle vehicle load limits are generally
decreased by the proposed formula. It is felt that
the new formula will satisfactorily protect the
bridge structures, but there is a real concern as to
its effect on pavements.
A notice titled "Report on Bridge Formula
Development for Regulating Vehicle Weight
Limitations" which contained the new Bridge
Formula and its supportive Executive Summary
was published in the Federal Register, Vol. 50, No.
182 dated September 19, 1985, to soliCit
comments. In general, the responses reflected
comments regarding a variety of items directly
associated with the impact of the new formula. A
majority of the respondents felt that more
information and more study are needed. while less
than half of the responses reflected opposition to
the new formula with or without modification.
Further evaluati.on of the current fOID1Ula. the
proposed formula, and alternative bridge
overstress procedures is being conducted as part
of an overall truck size and weight research
program within FHWA. Two particular studies
tlmt will include bridge fonnula analyses are:
@
@
'Truck Size and Weight Policy Impact Study."
This study will specifically analyze industry
impacts of potenUallegislative changes in the
gross weight C&p. the Bridge Formula, and
grandfather r.ghts.
"Impact of Truck Characteristics on
Pavements." This study will further examine
pavement aspects of truck size and weight
policy. Much ofthegovernmentalhighwaycost
PROPOSED BRIDGE FORMULA
- -@--EXISTING BRIDGE FORMULA
(w w '54
tw
fw
t
IIr
IIr
+L
62. .. ~
500 (IN + ~ 2. N + 36\
\"N-!
,.. ')
"",/,/
120
-i----+---+----+---~
100
U) 80
0..
-~
-3:
60 -+-_ _
40 -+--
W·
4------+----~~--~+-----~----~------r_--__4
20
o
o
8
20
40
so
80
100
120
140
L(FTJ
Graphical comparison of proposed bridge formula to existing bridge formula
FIGURE 1
229
lmpacts of any change in size and weight policy
are pavement related and yet little is really
known about the relationships of various
truck characteristics to pavement wear. This
study will build on similar work being done by
the Canadians and will provide damage
relationships to better estimate pavement
impacts of longer combinations. It also will
address system wide procedures for assessing
pavement costs of various size and weight
policy options including alternative bridge
formulas or procedures.
The future size and weight policy is a predominant
truck issue currently facing FHWA Recognizing
this. a Truck Technical Coordinating Group
[TreG) has been established to review current
truck Size and weight related research in FHWA.
NCHRP. and other work such as the Canadian
Heavy Vehicle Weights and Dimensions Study.
and to identify research needs where gaps
currently exist.
FHWA believes that it is critical to focus FHWA
truck research on the most important research
gaps and coordinate it with SHRP. NCHRP, and
other work such as the Canadia.'"1 Truck Research.
230
SESSION 7
MONITORING CONCEPTS AND TECHNOLOGY
Chairman:
P. Toogood
British Columbia MiniStry of
Transportation and Highways
Canada
231